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Katyanochek1 [597]
2 years ago
15

The axis of symmetry for a parabola with x intercepts (-8,0) & (12,0)

Mathematics
1 answer:
ahrayia [7]2 years ago
6 0

12-(-8)=20

x axis = 20:2 = 10

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A particle moving in a planar force field has a position vector x that satisfies x'=Ax. The 2×2 matrix A has eigenvalues 4 and 2
andrey2020 [161]

Answer:

The required position of the particle at time t is: x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}

Step-by-step explanation:

Consider the provided matrix.

v_1=\begin{bmatrix}-3\\1 \end{bmatrix}

v_2=\begin{bmatrix}-1\\1 \end{bmatrix}

\lambda_1=4, \lambda_2=2

The general solution of the equation x'=Ax

x(t)=c_1v_1e^{\lambda_1t}+c_2v_2e^{\lambda_2t}

Substitute the respective values we get:

x(t)=c_1\begin{bmatrix}-3\\1 \end{bmatrix}e^{4t}+c_2\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}

x(t)=\begin{bmatrix}-3c_1e^{4t}-c_2e^{2t}\\c_1e^{4t}+c_2e^{2t} \end{bmatrix}

Substitute initial condition x(0)=\begin{bmatrix}-6\\1 \end{bmatrix}

\begin{bmatrix}-3c_1-c_2\\c_1+c_2 \end{bmatrix}=\begin{bmatrix}-6\\1 \end{bmatrix}

Reduce matrix to reduced row echelon form.

\begin{bmatrix} 1& 0 & \frac{5}{2}\\ 0& 1 & \frac{-3}{2}\end{bmatrix}

Therefore, c_1=2.5,c_2=1.5

Thus, the general solution of the equation x'=Ax

x(t)=2.5\begin{bmatrix}-3\\1\end{bmatrix}e^{4t}-1.5\begin{bmatrix}-1\\1 \end{bmatrix}e^{2t}

x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}

The required position of the particle at time t is: x(t)=\begin{bmatrix}-7.5e^{4t}+1.5e^{2t}\\2.5e^{4t}-1.5e^{2t}\end{bmatrix}

6 0
3 years ago
A group of people were asked if they had run a red light in the last year. 315 responded "yes", and 190 responded "no".
Iteru [2.4K]

Answer:

0.624

Step-by-step explanation:

Number who have run a red light = 315

Number who haven't run a red light = 190

From the data :

The total number of people sampled = total possible outcome = (315 + 190) = 505

Selecting a person at random, probability that the selected person has run a red light :

P = required outcome / Total possible outcomes

Required outcome = Number who have run a red light = 315

P(having run a red light) = 315 / 505 = 0.624

6 0
3 years ago
The measure of the supplement of an angle is 20° more than three times the measure of the original angle. find the measures of t
viva [34]

If the original angle is x degrees then its supplement is 180 - x degrees.

we have the equation:-

180 - x = 3x + 20

160 = 4x

x = 40

The original angle is 40 degrees and its supplement is 140 degrees

3 0
3 years ago
Plzzzz help me ??!?!?!??
True [87]

Pythagorean Theorem is for right triangles

 right triangles have a 90 degree angle in them

 D is a right triangle

5 0
3 years ago
Read 2 more answers
Can you explain with steps
bonufazy [111]

Answer:

Yep

1. Click ask question at the top

2. type your question or add a picture

3. then click Ask

but you messed up in step 2 because you didn’t add a picture! Your Welcome

Step-by-step explanation:

5 0
2 years ago
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